Equations and Properties of Circles Quiz

Test your knowledge on circle equations & properties in analytic geometry with these 21 questions. Explore standard forms, center-radius, and more!

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What is the standard form of the equation of a circle?

x^2 + y^2 = r^2

y = mx + b

y^2 = ax^2 + bx + c

y = a(x - h)^2 + k

2 answered

Which of the following is the center-radius form of the equation of a circle?

(x - h)^2 + (y - k)^2 = r^2

x^2 + y^2 = r^2

y = mx + b

y = a(x - h)^2 + k

2 answered

Which of the following is the equation of a circle with center (0,0) and radius 3?

x^2 + y^2 = 9

x^2 + y^2 = 3

y = 3x

y = x^2

1 answered

Which of the following is the equation of a circle with center (2,-5) and radius 7?

(x - 2)^2 + (y + 5)^2 = 7^2

(x + 2)^2 + (y - 5)^2 = 7

(x - 2)^2 + (y - 5)^2 = 7

(x + 2)^2 + (y + 5)^2 = 7^2

1 answered

What is the equation of the circle with center (1,4) and radius 3?

(x - 1)^2 + (y - 4)^2 = 3^2

(x + 1)^2 + (y - 4)^2 = 3

(x - 1)^2 + (y + 4)^2 = 3

(x + 1)^2 + (y + 4)^2 = 3^2

1 answered

What is the standard form of the equation of a circle with center (-2,5) and radius 4?

(x + 2)^2 + (y - 5)^2 = 16

(x - 2)^2 + (y + 5)^2 = 4

(x + 2)^2 + (y - 5)^2 = 4

(x - 2)^2 + (y + 5)^2 = 16

1 answered

What is the equation of the circle with center (3,-1) and radius 2?

(x - 3)^2 + (y + 1)^2 = 4

(x + 3)^2 + (y - 1)^2 = 2

(x - 3)^2 + (y + 1)^2 = 2

(x + 3)^2 + (y - 1)^2 = 4

1 answered

What does the radius represent in the equation of a circle?

The distance from the center to any point on the circle

The slope of the circle

The x-coordinate of the center

The y-coordinate of the center

1 answered

What is the equation of the circle with center (2, -3) and radius 5?

(x - 2)^2 + (y + 3)^2 = 5^2

(x + 2)^2 + (y - 3)^2 = 5

(x - 2)^2 + (y - 3)^2 = 5

(x + 2)^2 + (y + 3)^2 = 5^2

1 answered

#10

What is the equation of the circle passing through the points (1,2), (3,4), and (5,6)?

(x - 1)(x - 3)(x - 5) + (y - 2)(y - 4)(y - 6) = 0

(x - 1)^2 + (y - 2)^2 = (x - 3)^2 + (y - 4)^2 = (x - 5)^2 + (y - 6)^2

x^2 + y^2 + 2x + 4y - 39 = 0

x^2 + y^2 - 10x - 12y + 39 = 0

1 answered

#11

Which of the following is the center-radius form of the equation of a circle with center (4,-2) and radius 6?

(x - 4)^2 + (y + 2)^2 = 6

(x + 4)^2 + (y - 2)^2 = 36

(x - 4)^2 + (y + 2)^2 = 36

(x + 4)^2 + (y - 2)^2 = 6^2

1 answered

#12

In the equation of a circle, what does the value 'h' represent?

The y-coordinate of the center

The x-coordinate of the center

The radius

The slope

1 answered

#13

What is the equation of the circle with center (0,0) and passing through the point (5,12)?

x^2 + y^2 = 169

x^2 + y^2 = 144

x^2 + y^2 = 25

x^2 + y^2 = 13

1 answered

#14

In the equation of a circle, what does the value 'k' represent?

The x-coordinate of the center

The y-coordinate of the center

The radius

The slope

1 answered

#15

What is the general equation of a circle?

x^2 + y^2 + Dx + Ey + F = 0

x^2 - y^2 = r^2

y = mx + b

y = a(x - h)^2 + k

1 answered

#16

What is the equation of a circle with center (-3,4) and passing through the point (2,1)?

(x + 3)^2 + (y - 4)^2 = 50

(x - 3)^2 + (y + 4)^2 = 50

(x + 3)^2 + (y - 4)^2 = 25

(x - 3)^2 + (y + 4)^2 = 25

1 answered

#17

What is the equation of a circle with center (-1,3) and radius 5?

(x + 1)^2 + (y - 3)^2 = 25

(x - 1)^2 + (y + 3)^2 = 25

(x + 1)^2 + (y - 3)^2 = 5

(x - 1)^2 + (y + 3)^2 = 5

1 answered

#18

What is the standard form of the equation of a circle in three-dimensional space?

x^2 + y^2 + z^2 = r^2

x^2 + y^2 = r^2

x^2 + y^2 + z = r

x^2 + y = r^2

1 answered

#19

In the equation of a circle, what does the value 'r' represent?

The distance from the center to any point on the circle

The slope of the circle

The x-coordinate of the center

The y-coordinate of the center

1 answered

#20

What is the equation of a circle with center (-2, 5) and passing through the point (1, -1)?

(x + 2)^2 + (y - 5)^2 = 40

(x - 2)^2 + (y + 5)^2 = 40

(x + 2)^2 + (y - 5)^2 = 25

(x - 2)^2 + (y + 5)^2 = 25

1 answered

#21

What is the equation of the circle with center (3, 7) and radius 8?

(x - 3)^2 + (y - 7)^2 = 64

(x + 3)^2 + (y + 7)^2 = 64

(x - 3)^2 + (y + 7)^2 = 64

(x + 3)^2 + (y - 7)^2 = 64

1 answered

Equations and Properties of Circles Quiz

What is the standard form of the equation of a circle?

Which of the following is the center-radius form of the equation of a circle?

Which of the following is the equation of a circle with center (0,0) and radius 3?

Which of the following is the equation of a circle with center (2,-5) and radius 7?

What is the equation of the circle with center (1,4) and radius 3?

What is the standard form of the equation of a circle with center (-2,5) and radius 4?

What is the equation of the circle with center (3,-1) and radius 2?

What does the radius represent in the equation of a circle?

What is the equation of the circle with center (2, -3) and radius 5?

What is the equation of the circle passing through the points (1,2), (3,4), and (5,6)?

Which of the following is the center-radius form of the equation of a circle with center (4,-2) and radius 6?

In the equation of a circle, what does the value 'h' represent?

What is the equation of the circle with center (0,0) and passing through the point (5,12)?

In the equation of a circle, what does the value 'k' represent?

What is the general equation of a circle?

What is the equation of a circle with center (-3,4) and passing through the point (2,1)?

What is the equation of a circle with center (-1,3) and radius 5?

What is the standard form of the equation of a circle in three-dimensional space?

In the equation of a circle, what does the value 'r' represent?

What is the equation of a circle with center (-2, 5) and passing through the point (1, -1)?

What is the equation of the circle with center (3, 7) and radius 8?

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